A handpiece of an electric toothbrush is known, for example, from DE 199 40 369 C2. Regularly accommodated in the housings of the handpieces of electric toothbrushes are, in addition to the electric motor of the drive unit, batteries or rechargeable batteries for supplying power to the drive unit, which means that the housing has to be opened in order to be able to remove and replace the batteries or rechargeable batteries. For this purpose it is known to provide on the rearward end of the housing remote from the toothbrush head a housing opening which can be closed with a housing cover. It is also known for provision to be made on the forward end close to the toothbrush head for a housing cover which closes a housing opening through which the drive unit can be inserted from above into the housing. However, such a housing cover on the top side of the handpiece has to be securely connected with the housing by frictional and/or positive engagement in order to be able to absorb the cleaning forces introduced via the brush tube and ensure a moisture- and liquid-proof closure of the housing also under load. In this arrangement, the brush tube is coupled to the housing cover, the drive train then extending from the drive unit accommodated in the housing through the housing cover and the brush tube to the brush head. It is also known to lock such a forward-end housing cover in the region of the drive train securely to the housing by means of snap-action detent elements in order to be able to absorb the forces introduced. However, such a snap-fit connection makes it difficult to release the cover again, for example in order to be able to remove the drive unit or batteries or rechargeable batteries accommodated in the housing.